How to exclude an object from Freestyle render?
So you want freestyle on the plane but not the plane :)

This is very easy to do. Add the plane to an object group. Select it and press CtrlG.

Now in the Scene tab of the Properties panel scroll down to the "Freestyle Line Set" section, and add Group to the "Selection By:" setting. (outlined in red in the image below)


Set the group you made earlier as the "Group" (the group field will be on the bottom).
Now depending on which plane you grouped, click the "Inclusive" box if you grouped your airplane; because you want to only include objects in the group in this freestyle lines. Conversely  if you grouped the ground plane click the "Exclusive" box, to exclude the ground plane from freestyle.